Details

sample430.0ms

Algorithm

intervals

Results

85.0ms	48×	body	2560	valid
51.0ms	90×	body	1280	valid
17.0ms	66×	body	640	valid
4.0ms	26×	body	320	valid
2.0ms	18×	body	160	valid
2.0ms	8×	body	80	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 32.3b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.8b	(- x (tan x))
1.9b	(- x (sin x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

8.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series180.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(/ (- x (sin x)) (- x (tan x)))
60.0ms	(- x (tan x))
42.0ms	(- x (sin x))

simplify159.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	685
2	4795	685
3	5001	685

prune189.0ms

Filtered

89 candidates to 63 candidates (70.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	3	90

Merged error: 0.0b

Counts

90 → 3

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
15.6b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `sum-log` `flip--` `associate--r+`

Counts

3 → 66

Calls

3 calls:

5.0ms	(* 27/2800 (pow x 4))
5.0ms	(* 9/40 (pow x 2))
7.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series111.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* 27/2800 (pow x 4))
29.0ms	(* 9/40 (pow x 2))
45.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify45.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	273	349
1	1123	318
2	5001	315

prune130.0ms

Filtered

75 candidates to 46 candidates (61.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	73	5	78

Merged error: 0.0b

Counts

78 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

15.4b	(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))
15.6b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
15.6b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
15.6b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-log-exp`
6×	`diff-log`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`cbrt-prod` `sub-neg` `sum-log` `associate--r+`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 55

Calls

4 calls:

7.0ms	(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))
7.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
7.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
7.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series285.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))
44.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
46.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
47.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify106.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	223	719
1	715	659
2	3152	657
3	5001	657

prune193.0ms

Filtered

67 candidates to 48 candidates (71.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	67	5	72

Merged error: 0.0b

Counts

72 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

15.4b	(cbrt (- (- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4))) 1/2))
15.6b	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))
15.6b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
15.6b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-log-exp`
7×	`add-sqr-sqrt` `*-un-lft-identity`
5×	`cbrt-prod` `add-cube-cbrt` `diff-log`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`sub-neg`
2×	`cbrt-div` `sum-log` `associate--r+`
1×	`pow1/3` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 55

Calls

4 calls:

6.0ms	(cbrt (- (- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4))) 1/2))
4.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))
7.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
7.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series348.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(cbrt (- (- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4))) 1/2))
114.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))
44.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
48.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify166.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	311	696
1	1011	646
2	4839	638
3	5001	638

prune205.0ms

Filtered

67 candidates to 49 candidates (73.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	67	5	72

Merged error: 0.0b

Counts

72 → 5

regimes67.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.9b

bsearch66.0ms

Steps

Iters	Range		Point
7	0.00999808388340962	0.475758948552502	0.029426069937885588
9	-164485.30314980465	-0.009598081335721272	-0.027401026806997613

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	13
1	32	13

end0.0ms

sample6.6s

Algorithm

intervals

Results

4.2s	1624×	body	2560	valid
1.6s	2730×	body	1280	valid
472.0ms	1911×	body	640	valid
147.0ms	940×	body	320	valid
55.0ms	440×	body	160	valid
25.0ms	355×	body	80	valid